Sunday, December 30, 2018

Twin Paradox: Tale of twins


Hello and welcome back to my blog ‘Physics Talk’.

My previous post was about special relativity, which said that the laws of physics are equivalent in every frame of reference irrespective of their speeds and the speed of light in vacuum has a fixed value. One of the consequences of the Special Relativity is the Time Dilation. It is the difference in the time measured for the occurrence of an event between two frames of references. This gave birth to a paradox known as Twin Paradox.

Twin Paradox is a thought experiment where two twins, suppose ‘A’ and ‘B’, are taken into account (they would have the same age). Consider that ‘B’ is good in studies and later at the age of 30 he becomes an astronaut. On the other hand ‘A’ is making his living by doing something on the earth. Suppose ‘B’ boards a spacecraft on the earth, to go to a distant planet. The spacecraft moves with speed close to the speed of light. ‘B’ goes to the distant planet and comes back to the earth. But when he returns one of them would be younger than the other according to the time dilation phenomenon of special relativity. 

Who do you think would be younger?

From ‘A’s frame of reference, who is on earth, ‘B’ is moving and he himself is stationary. Here, the length travelled by ‘B’ in the spacecraft would be less than what will be measured by ‘A’, due to the length contraction phenomenon of special relativity. Therefore, in ‘A’s frame of reference, the time taken by ‘B’ for the whole journey would be less than what will be measured by ‘A’. Therefore, ‘A’ would be older than ‘B’.

 Image by Kilian Kluge (Cirdan 18:21, 19 Jun 2005 (UTC) ) Twinparadox overview
license CC BY-SA 3.0
                                               
 Is it really true?

As frames of references are relative, everybody can consider themselves to be stationary. As a result, ‘B’ can also claim that he is stationary and the earth and ‘A’ are moving backward and forward. Therefore in ‘B’s frame of reference he would be older than ‘A’. But both cannot be younger and older than the other at the same time. Therefore, one of them must be wrong. This creates the paradox.

One of the explanation of the paradox is the role of acceleration. To make the return journey ‘B’ must stop the spaceship and fire the engines in reverse direction. Therefore, he would feel the acceleration. This would make his journey non inertial (it is a frame of reference which is undergoing acceleration with respect to an inertial frame.). But the special theory of relativity were derived for inertial frames (this is a frame of reference where net force acting or acceleration is zero) of references. Hence, ‘A’ would be older than ‘B’.

But this explanation can be contradicted with the three twin experiment where suppose ‘A’ is on earth, ‘B’ is moving from the earth in spaceship towards some planet ‘M’, and ‘C’ is moving from planet ‘M’ towards earth in another spaceship. ‘B’ and ‘C’ meet in between. There they synchronize their clocks and move forward (note: they do not stop, they synchronize their clocks while moving at the same speed). When ‘C’ would reach the earth, time experienced by him would be less than time measured by ‘A’ for the whole journey. There is no acceleration here. Therefore, acceleration cannot be the correct explanation of the paradox.

The most accepted explanation is that of the role of inertial reference frames. ‘A’, who is on earth is in one inertial reference frame throughout, while ‘B’ is in two inertial reference frames as he stops and returns. This is argued to be the explanation for ‘A’ being the stationary observer.

Some also use General Relativity and Doppler Effect to explain this paradox, but it is not necessary as special relativity is sufficient to explain this paradox.

Sunday, December 16, 2018

Special Relativity: History and its Consequences


Hello Physics enthusiasts! Here is my new blog post and I would like to begin by asking you all a question.
A person flashes a light inside the train. You are on the platform and the train passes by you at that moment. Will the speed of light for the person flashing the light and you be the same?
You will know that after reading my new post on the Special Relativity Theory. Enjoy!!!!
Special Theory of Relativity or Special Relativity was introduced on the paper "On the Electrodynamics of Moving Bodies" by Albert Einstein in 1905. There are many factors that led to the Special Relativity, but the most prominent ones are the inconsistency of Newtonian Mechanics with Maxwell's Equations and also the lack of experimental corroboration for the ether theory.
Let’s take the example to explain the inconsistency of Newtonian Mechanics with Maxwell's Equations. A person throws a ball to another person inside a moving train towards the motion of the train at a speed of 10 m/s. The train is moving at 60 m/s. An observer inside the train observes the ball to travel at speed 10 m/s because for him the train is at rest and only the ball is moving, but for an observer outside the train the speed of the ball is (10+60) 70 m/s because for him both the train and the ball are moving the same direction. This is Newtonian Mechanics where time is absolute in each frame of references. Now consider the situation in the beginning of the blog, according to Newtonian Mechanics the speed of light for an observer outside the train should change. But in Maxwell's Theory the speed of light has a certain fixed value. Therefore, both the theories are contradicting each other.
To reconcile Newton's Laws with the Maxwell's Equations Aether theory came out. It was said that a substance called Aether was present everywhere in the universe. Just like sound waves require a medium to travel, Ether was the medium in which light (electromagnetic waves) travels. But later experiment performed by Michelson and Morley, by comparing speed of light in two different situations, showed no proof of the presence of Aether as the speeds came out to be equal.
Albert Einstein said that there was no need for the aether if we are willing to renounce the idea of absolute time. Therefore, he came up with the idea of Special Relativity. It had two postulates. The first is that the laws of physics apply to everything everywhere, whatever their speeds are. The second is that speed of light in vacuum is constant for all observers irrespective of their speeds. There are many consequences of this theory. The first one is called the length contraction. It is the phenomenon of contraction of length of an object with respect to an observer whose speed with respect to the object is zero. Suppose an object moves with certain speed and observer observes it from outside. The observer would see that the length of the object reduces as the object goes past him/her. But this is only significant for speeds closer to the speed of light. For smaller speeds the effect can be neglected.
Second consequence is the time dilation. It is the difference in time measured, for the occurrence of an event, between two observers moving relative to each other. Suppose in a moving spacecraft a light is flashed. For an observer outside the distance traveled by light is greater than the distance measured by an observer inside, as the spacecraft is itself moving. Since time is equal to distance by speed and speed of light constant, therefore the time measured by the outside observer is greater than time measured by the observer inside the spacecraft. This is also significant for speeds closer to the speed of light.
Another consequence is the increase of mass of a body when the body is travelling at speeds closer to speed of light. Mathematics shows that mass of a body reaches infinity if speed of light is achieved. The famous mass energy equivalence is also the result of special relativity. This tells us that mass can be converted into energy, but it also tells us that if energy increases so does the mass, which is a resistance to acceleration and speed. Therefore, more is the speed greater is the mass and greater will be the energy required to maintain the speed. This is the reason that speed of an object cannot cross the value of speed of light in vacuum.
You might have a question that why does light travels at that speed?
The answer is that light is made up of energy packets called photons which do not have any mass.
Einstein's theory was called "Special" Relativity because it couldn't explain the effect of Newton's Law of Gravity. Consider a situation where the sun suddenly disappears from our solar system. Maxwell's theory states that it would take around eight minutes for the earth to get dark (distance between earth and sun by speed of light is the time taken, here eight minutes).But Newton's Law states that earth would immediately feel the absence of sun's attraction and fly out of orbit. Here information traveled immediately, that is with speed greater than speed of light, which was inconsistent with special relativity. Special Relativity is accepted where gravitational effects on the body are negligible.
But don’t think that Newton’s Laws are of no use. They are still used where the speeds are much lesser than the speed of light.


Reference:
A Brief History of Time by Stephen Hawking


Friday, December 14, 2018

Schrodinger's Cat: An Experiment of Uncertainities


There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.”- Erwin Schrödinger

Hello and welcome to my new blog “Physics Talk” and here is my first post about the Schrodinger’s Cat.

P.S- It’s not about someone’s cat, for those of you who has no idea what it is. But worry not that’s where I come in to solve your scientific doubts. I can assure you that after reading my post you will not just learn a new thing but will also be interested to know more.

So lets begin…

Schrodinger’s Cat was a thought experiment devised by Erwin Schrodinger, a physicist who is famous for his works in Quantum Mechanics. In the 1920s, physicist Neils Bohr gave the Copenhagen Interpretation of Quantum Mechanics. It stated that a physical system does not have definite properties, like spin, unless being measured. Quantum mechanics only predicts the probability of the property. If the property is measured then the wave function collapses and a definite value of the property is obtained. Schrodinger stated the Schrodinger’s Cat experiment to show the absurdity of the Copenhagen Interpretation.

He stated that if a cat is locked in a sealed steel chamber containing the following devices: a gieger counter for counting the amount of radioactive decay and a radioactive element. In one hour one of the atoms of the radioactive element may decay or may not. If it decays it will release an atomic particle, which in turn will hit the gieger counter which will release a hammer and smash a flask containing hydrocyanic acid (poison), this will kill the cat. If the radioactive element doesn’t break down then the cat will be alive after an hour. According to Copenhagen interpretation, the cat may be both alive and dead after an hour. It can only be known if the chamber is opened. But by opening the box the experiment is interfered. Therefore, without interfering with the experiment the state of the cat can be known as the superposition of different states (dead and alive just like a zombie).

Schrodinger said that it was ridiculous. An object cannot be both dead and alive. Therefore he used this experiment to show the fault in Copenhagen Interpretation. Even Einstein agreed with Schrodinger. He even wrote Schrodinger a letter acknowledging the experiment. Although there are many articles on the internet stating that Schrodinger agreed with the Copenhagen Interpretation, but actually that was not the case.

Today there are experiments which shows that the Copenhagen Interpretation is correct for microscopic particles like electrons, positrons, etc.

So what do you think, the cat will be dead or alive?